Does anyone knows if dream tickets carry over or will expire after this event?

The rules in using the Dream Tickets are stated on the blue banner of your main page.The last point would be the most useful to your question:

"You will not be able to use Dream(S) Tickets once the Dream Chests become unavailable. Please be aware that you will not be able to use any Dream(S) Tickets earned during 'The Doomsday Tower: Revelations' event with future Dream Chests."

In other words, if you don't use them now or before July 26th, your Dream Tickets will be gone for good.

they should have given out way more ticketsthe most anyone can get is what, like 3

Yep... It's a joke how little you can get, it's almost like a premium ticket at that point. What makes the Dream tickets worse though, is that you can't even use them in Leana's Shop like Premium tickets.